A numerical characterization of the extremal Betti numbers of t-spread strongly stable Ideals

2021/05/25 by Amata, Luca, Ficarra, Antonino, Crupi, Marilena · 1 citation
#05E40 #13B25 #13D02 #16W50 #68W30 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2105.11944

Abstract

Let K be a field and let S=K[x₁,…,x_n] be a standard polynomial ring over a field K. We characterize the extremal Betti numbers, values as well positions, of a t-spread strongly stable ideal of S. Our approach is constructive. Indeed, given some positive integers a₁,…,a_r and some pairs of positive integers (k₁,ℓ₁),…,(k_r,ℓ_r), we are able to determine under which conditions there exist a t-spread strongly stable ideal I of S with β_{ki, kiℓi}(I)=a_i, i=1, …, r, as extremal Betti numbers, and then to construct it.

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